Problem: Simplify the following expression: $ q = -10 + \dfrac{x - 4}{6x} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6x}{6x}$ $ \dfrac{-10}{1} \times \dfrac{6x}{6x} = \dfrac{-60x}{6x} $ Therefore $ q = \dfrac{-60x}{6x} + \dfrac{x - 4}{6x} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-60x + x - 4}{6x} $ $q = \dfrac{-59x - 4}{6x}$